chapter 8 consumer mathematics and financial...

Chapter 8 Consumer Mathematics and Financial Management

356

Check Points 8.1

1. Step 1: 1

1 8 0.1258

Step 2: 0.125 100 12.5 Step 3: 12.5%

2. 0.023 2.3%

3. a. 67% 0.67

b. 250% 2.50 2.5

4. a. 6% of $1260 0.06 $1260 $75.60 The tax paid is $75.60

b. $1260.00 $75.60 $1335.60 The total cost is $1335.60

5. a. 35% of $380 0.35 $380 $133 The discount is $133

b. $380 $133 $247 The sale price is $247

6. Step 1. Determine the adjusted gross income. Adj. gross income = Gross income – Adjustments Adj. gross income $40,000 $1000

$39,000

Step 2. Determine the taxable income. Since the total deduction of $4800 is less than the standard deduction of $5450, use $5450. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $39,000 ($3500 $5450)

$30,050

Step 3. Determine the income tax. Tax Computation

0.10(8025) 0.15(30,050 8025)

$4106.25

Income tax = Tax Computation – Tax credits Income tax $4106.25 $0

$4106.25

7. a. Percent of increase =amount of increase

original amount

2 23 3

40.66 66 %

6

b. Percent of decrease = amount of decrease

original amount

4

0.4 40%10

8. Amount of decrease: $940 $611 $329 amount of decrease $329

0.35 35%original amount $940

There was a 35% decrease from 1998 to 1999.

9. Amount of increase: 12% 10% 2% amount of increase 2%

0.2 20%original amount 10%

There was a 20% increase for this episode.

10. a. 20% of $1200 0.20 $1200 $240 Taxes for year 1 are $1200 $240 $960 20% of $960 0.20 $960 $192 Taxes for year 2 are $960 $192 $1152

b. $1200 $1152 $48

0.04 4%$1200 $1200

Taxes for year 2 are 4% less than the original amount.

Exercise Set 8.1

1. 2

2 5 0.4 40%5

2. 3

3 5 0.6 60%5

3. 1

1 4 0.25 25%4

4. 3

3 4 0.75 75%4

5. 3

3 8 0.375 37.5%8

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

ISM: Thinking Mathematically Section 8.1

357

6. 7

7 8 0.875 87.5%8

7. 1

1 40 0.025 2.5%40

8. 3

3 40 0.075 7.5%40

9. 9

9 80 0.1125 11.25%80

10. 13

13 80 0.1625 16.25%80

11. 0.59 = 59%

12. 0.96 = 96%

13. 0.3844 = 38.44%

14. 0.003 = 0.3%

15. 2.87 = 287%

16. 9.83 = 983%

17. 14.87 = 1487%

18. 19.63 = 1963%

19. 100 = 10,000%

20. 95 = 9500%

21. 72% = 0.72

22. 38% = 0.38

23. 43.6% = 0.436

24. 6.25% = 0.0625

25. 130% = 1.3

26. 260% = 2.6

27. 2% = 0.02

28. 6% = 0.06

29. 1

% 0.5% 0.0052

30. 3

% 0.75% 0.00754

31. 5

% 0.625% 0.006258

32. 1

% 0.125% 0.001258

33. 1

62 % 62.5% 0.6252

34. 1

87 % 87.5% 0.8752

35. A PB 0.03 200

6

A

A

36. A PB 0.08 300

24

A

A

37. A PB 0.18 40

7.2

A

A

38. A PB 0.16 90

14.4

A

A

39. A PB 3 0.60

3 0.60

0.60 0.605

B

B

B

40. A PB 8 0.40

8 0.40

0.40 0.4020

B

B

B

41. A PB 40.8 0.24

40.8 0.24

0.24 0.24170

B

B

B

42. A PB 51.2 0.32

51.2 0.32

0.32 0.32160

B

B

B


Chapter 8: Consumer Mathematics and Financial Management ISM: Thinking Mathematically

358

43. A PB 3 15

3 15

15 150.2

20%

P

P

P

P

44. A PB 18 90

18 90

90 900.2

20%

P

P

P

P

45. A PB 0.3 2.5

0.3 2.5

2.5 2.50.12

12%

P

P

P

P

46. A PB 0.6 7.5

0.6 7.5

7.5 7.50.08

8%

P

P

P

P

47. a. (0.06)(32,800) = $1968

b. 32,800 + 1968 = $34,768

48. a. (0.07)(96) = $6.72

b. 96 + 6.72 = $102.72

49. a. (0.12)(860) = $103.20

b. 860 – 103.20 = $756.80

50. a. (0.40)(16.50) = $6.60

b. 16.50 – 6.60 = $9.90


$71,000

Step 2. Determine the taxable income. Since the total deduction of $35,200 is greater than the standard deduction of $5450, use $35,200.

Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $71,000 ($3500 $35, 200)

$32,300


0.10(8025) 0.15(32,300 8025)

$4443.75


$4443.75


$68,000

Step 2. Determine the taxable income. Since the total deduction of $13,700 is greater than the standard deduction of $5450, use $13,700. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $68,000 ($3500 $13,700)

$50,800


0.10(8025) 0.15(32,550 8025)

0.25(50,800 32,550)

$9043.75


$9043.75


$50,000

Step 2. Determine the taxable income. Since the total deduction of $6500 is less than the standard deduction of $8000, use $8000. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $50,000 ($3500 3 $8000)

$31,500


0.10(11, 450) 0.15(31,500 11,450)

$4152.50


$2152.50



359


$38,500

Step 2. Determine the taxable income. Since the total deduction of $4400 is less than the standard deduction of $8000, use $8000. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $38,500 ($3500 2 $8000)

$23,500


0.10(11,450) 0.15(23,500 11,450)

$2952.50


$452.50

55. FICA tax 0.0765(102,000) 0.0145(120,000 102,000)

$8064

56. FICA tax 0.0765(102,000) 0.0145(140,000 102,000)

$8354

57. FICA tax 0.0765(102,000) 0.0145(150,000 102,000)

$8499

Since, this person is self-employed the FICA rate is doubled: $8499 2 $16,998

58. FICA tax 0.0765(102,000) 0.0145(160,000 102,000)

$8644

Since, this person is self-employed the FICA rate is doubled: $8644 2 $17,288

59. a. FICA tax 0.0765(20,000)

$1530

b. Step 1. Determine the adjusted gross income. Adj. gross income = Gross income – Adjustments Adj. gross income $20,000 $0 $20,000 Step 2. Determine the taxable income. The standard deduction is $5450. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $20,000 ($3500 $5450)

$11,050


0.10(8025) 0.15(11,050 8025)

$1256.25


$1256.25

c. 1530 1256.25

0.139 13.9%20,000

60. a. FICA tax 0.0765(18,000)

$1377

b. Step 1. Determine the adjusted gross income. Adj. gross income = Gross income – Adjustments Adj. gross income $18,000 $0 $18,000 Step 2. Determine the taxable income. The standard deduction is $5450. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $18,000 ($3500 $5450)

$9050


0.10(8025) 0.15(9050 8025)

$956.25


$956.25

c. 1377 956.25

0.130 13.0%18,000



360

61. 974 624

0.561 56.1%624

62. 589 387

0.522 52.2%387

63. 93 62

0.5 50.0%62

64. 682 460

0.483 48.3%460

65. 840 714

0.15 15%840

66. 380 266

0.30 30%380

67. Amount after first year = 10,000 – (0.3)(10,000) = $7000 Amount after second year = 7000 + (0.4)(7000) = $9800 Your adviser is not using percentages properly. Actual change: 10,000 9800

0.02 2%10,000

decrease.

68. The salesman is misusing percentages. 100% 30% 70% 20% of 70% 0.70(0.20) 0.14 14%

Percent reduction 30% 14% 44%

76. does not make sense; Explanations will vary. Sample explanation: 20% of $80 is $16. This will make the total $96.

77. does not make sense; Explanations will vary. Sample explanation: A price can not drop more than 100%.

78. does not make sense; Explanations will vary. Sample explanation: Since 1.01 1.01 1.0201 the percent of increase is 2.01%.

79. does not make sense; Explanations will vary. Sample explanation: The increase is 30% 20% 10% 1

0.5 50%20% 20% 2

.

80. Tax owed = $3.40 $78,500

$2669$100 1

Discount = (0.03)(2669) = $80.07 Tax paid = 2669 – 80.07 = $2588.93

81. January sales = 60 $500 $30,000 Number of customers in February

60 (0.10)(60) 60 6 54

Price of washing machine in February 500 (0.20)(500) 500 100 $600

February sales = 54 $600 $32,400 $32,400 – $30,000 = $2400 increase.

Check Points 8.2

1. ($3000)(0.05)(1) $150I Prt

2. ($2400)(0.07)(2) $336I Prt

3. 41 2040 1 0.075 $2091

12A P rt

4. 1A P rt

6800 5000 1 2

6800 5000 10,000

1800 10,000

1800 10,000

10,000 10,000

0.18

18%

r

r

r

r

r

r

5. 1A P rt

6124000 1 0.08

4000 (1.04)

4000 (1.04)

1.04 1.043846.153

$3846.16

P

P

P

P

P

6. a. 5000 0.12 2 1200I Prt

The loan’s discount is $1200.

b. Amount received: $5000 $1200 $3800



361

c. I Prt

1200 3800 2

1200 7600

1200 7600

7600 76000.158

15.8%

r

r

r

r

r

Exercise Set 8.2

1. ($4000)(0.06)(1) $240I

2. ($7000)(0.05)(1) $350I

3. ($180)(0.03)(2) $10.80I

4. ($260)(0.04)(3) $31.20I

5. 9

($5000)(0.085) $318.7512

I

6. 18

($18,000)(0.075) $202512

I

7. 90

($15,500)(0.11) $426.25360

I

8. 60

($12,600)(0.09) $189360

I

9. 1 3000 1 0.07 2 $3420A P rt

10. 1 2000 1 0.06 3 $2360A P rt

11. 1 26,000 1 0.095 5 $38,350A P rt

12. 1 24,000 1 0.085 6 $36,240A P rt

13. 8121 9000 1 0.065 $9390A P rt

14. 9121 6000 1 0.045 $6202.50A P rt

15. 1A P rt

2150 2000 1 1

2150 2000 2000

150 2000

150 2000

2000 20000.075

7.5%

r

r

r

r

r

r

16. 1A P rt

3180 3000 1 1

3180 3000 3000

180 3000

180 3000

3000 30000.06

6%

r

r

r

r

r

r

17. 1A P rt

5900 5000 1 2

900 5000 10,000

900 10,000

900 10,000

10,000 10,000

0.09

9%

r

r

r

r

r

r

18. 1A P rt

14,060 10,000 1 2

14,060 10,000 20,000

4060 20,000

4060 20,000

20,000 20,000

0.203

20.3%

r

r

r

r

r

r

19. 1A P rt

9122840 2300 1

2840 2300 1725

540 1725

540 1725

1725 17250.313

31.3%

r

r

r

r

r

r



362

20. 1A P rt

6121820 1700 1

1820 1700 850

120 850

120 850

850 8500.141

14.1%

r

r

r

r

r

r

21. 1A P rt

6000 1 0.08 2

6000 (1.16)

6000 (1.16)

1.16 1.165172.414

$5172.42

P

P

P

P

P

22. 1A P rt

8500 1 0.07 3

8500 (1.21)

8500 (1.21)

1.21 1.217024.793

$7024.80

P

P

P

P

P

23. 1A P rt

14,000 1 0.095 6

14,000 (1.57)

14,000 (1.57)

1.57 1.578917.197

$8917.20

P

P

P

P

P

24. 1A P rt

16,000 1 0.115 5

16,000 (1.575)

16,000 (1.575)

1.575 1.57510158.7302

$10,158.74

P

P

P

P

P

25. 1A P rt

9125000 1 0.145

5000 (1.10875)

5000 (1.10875)

1.10875 1.108754509.583

$4509.59

P

P

P

P

P

26. 1A P rt

8122000 1 0.126

2000 (1.084)

2000 (1.084)

1.084 1.0841845.018

$1845.02

P

P

P

P

P

27. a. 8122000 0.07 $93.33I Prt

b. Amount received: $2000 $93.33 $1906.67

c. I Prt

81293.33 1906.67

93.33 1271.113

93.33 1271.113

1271.113 1271.1130.073

7.3%

r

r

r

r

r

28. a. 9123000 0.08 $180I Prt

b. Amount received: $3000 $180 $2820

c. I Prt

912180 2820

180 2115

180 2115

2115 21150.085

8.5%

r

r

r

r

r



363

29. a. 12,000 0.065 2 $1560I Prt

b. Amount received: $12,000 $1560 $10,440

c. I Prt

1560 10,440 2

1560 20,880

1560 20,880

20,880 20,880

0.075

7.5%

r

r

r

r

r

30. a. 20,000 0.085 3 $5100I Prt

b. Amount received: $20,000 $5100 $14,900

c. I Prt

5100 14,900 2

5100 44,700

5100 44,700

44,700 44,700

0.114

11.4%

r

r

r

r

r

31. 1A P rt

A P Prt

A P Prt

A P Prt

Pt PtA P

rPt

A Pr

Pt

32. 1A P rt

A P Prt

A P Prt

A P Prt

Pr PrA P

tPr

A Pt

Pr

33. 1

1

1 1

1

1

A P rt

P rtA

rt rtA

Prt

AP

rt

34. 1ntr

nA P

1

1 1

1

1

ntrn

nt ntr rn n

ntrn

ntrn

PA

AP

AP

35. a. I Prt

9

($4000)(0.0825)12

$247.50

b. $4000 + $247.50 = $4247.50

36. a. I Prt

7($20,000)(0.12)

12

$1400

b. $20,000 + $1400 = $21,400

37. 1A P rt

2000 1400 1 2

2000 1400 2800

600 2800

600 2800

2800 28000.214

21.4%

r

r

r

r

r

r



364

38. 1A P rt

1000 981.60 1 2

1000 981.6 1963.2

18.4 1963.2

18.4 1963.2

1963.2 1963.20.075

7.5%

r

r

r

r

r

r

39. 1A P rt

11472 960 1

12

1472 960 80

512 80

512 80

80 806.4

640%

r

r

r

r

r

r

40. 1A P rt

1851 552 1

12

851 552 46

299 46

299 46

46 466.5

650%

r

r

r

r

r

r

41. 1A P rt

3000 1 0.065 2

3000 (1.13)

3000 (1.13)

1.13 1.132654.867

$2654.87

P

P

P

P

P

42. 1A P rt

8000 1 0.055 2

8000 (1.11)

8000 (1.11)

1.11 1.117207.207

$7207.21

P

P

P

P

P

43. a. $8000 0.08 3 $1920I Prt

b. $8000 $1920 $6080

c.

1920 6080 3

1920 18, 240

19200.105 10.5%

18,240

I Prt

r

r

r

44. a. $20,000 0.06 4 $4800I Prt

b. $20,000 $4800 $15,200

c.

4800 15, 200 4

4800 60,800

48000.079 7.9%

60,800

I Prt

r

r

r

48. does not make sense; Explanations will vary. Sample explanation: This would be the amount of interest after one year.

49. does not make sense; Explanations will vary. Sample explanation: The Banker’s rule produces a greater amount of interest.

50. does not make sense; Explanations will vary. Sample explanation: The principal should be rounded up to $3846.16 to make sure there is enough money.

51. makes sense

52. 1A P rt

2 1

12

2 1

1

1

1

1

P P rt

P rtP

P Prt

rt

rt

r r

tr

tr



365

53. a. 1A P rt

5000 1 0.055

5000 275

A t

A t

b. The slope is 275. This means the rate of change for the account is $275 per year.

Check Points 8.3

1. a. 5$1000(1 0.04) $1216.65A

b. $1216.65 $1000 $216.65

2. a. 4 10

0.04$4200 1 $6253.23

4A

b. $6253.23 $4200 $2053.23

3. a. 1nt

rA P

n

4(5)0.08

10,000 14

$14,859.47

A

b. rtA Pe

0.08(5)10,000

$14,918.25

A e

4.

1nt

AP

r

n

52 8

$10,000, 0.07, 52, 8

10,000 10,000$5714.25

1.7500133430.071

52

A r n t

P

5. a. 12 1

0.10$6000 1 $6628.28

12A

b. 1A P rt

6628.28 6000 1 1

6628.28 6000 6000

628.28 6000

628.28 6000

6000 60000.105

10.5%

r

r

r

r

r

r

6. 1 1n

rY

n

40.08

1 1 0.0824 8.24%4

Y

Exercise Set 8.3

1. a. 2$10,000(1 0.04) $10,816A

b. $10,816 – $10,000 = $816

2. a. 3$8000(1 0.06) $9528.13A

b. $9528.13 – $8000 = $1528.13

3. a. 2 4

8

0.05$3000 1

2

$3000(1.025)

$3655.21

A

b. $3655.21 – $3000 = $655.21

4. a. 2 5

0.04$4000 1

2A

10$4000(1.02)

$4875.98

b. $4875.98 – $4000 = $875.98

5. a. 4 5

20

0.06$9500 1

4

$9500(1.015)

$12,795.12

A

b. $12,795.12 – $9500 = $3295.12

6. a. 4 6

24

0.08$2500 1

4

$2500(1.02)

$4021.09

A

b. $4021.09 – $2500 = $1521.09

7. a. 12 3

36

0.045$4500 1

12

$4500(1.0038)

$5149.12

A

b. $5149.12 – $4500 = $649.12



366

8. a. 12 4

48

0.065$2500 1

12

$2500(1.0054)

$3240.05

A

b. $3240.05 – $2500 = $740.05

9. a. 360 2.5

900

0.085$1500 1

360

$1500(1.000236)

$1855.10

A

b. $1855.10 – $1500 = $355.10

10. a. 360 3.5

1260

0.085$1200 1

360

$1200(1.000236)

$1615.73

A

b. $1615.73 – $1200 = $415.73

11. a. 360 20

7200

0.045$20,000 1

360

$20,000(1.000125)

$49,189.30

A

b. $49,189.30 – $20,000 = $29,189.30

12. a. 360 20

7200

0.055$25,000 1

360

$25,000(1.000153)

$75,097.84

A

b. $75,097.84 – $25,000 = $50,097.84

13. a. 2(5)

0.05510,000 1

2

$13,116.51

A

b. 4(5)

0.05510,000 1

4A

≈ $13,140.67

c. 12(5)

0.05510,000 1

12

$13,157.04

A

d. 0.055(5)10,000

$13,165.31

A e

14. a. 2(10)

0.0655000 1

2A

$9479.19

b. 410

0.0655000 1 $9527.79

4A

c. 12(10)

0.0655000 1

12A

= $9560.92

d. 0.065(10)5000A e 9577.70

15. 12(3)

0.0712,000 1

12

14,795.11 (7% yield)

A

0.0685(3)12,000

14,737.67 (6.85% yield)

A e

Investing $12,000 for 3 years at 7% compounded monthly yields the greater return.

16. 4 4

0.08256000 1

4A

$8317.84 (8.25% yield) 2 4

0.0836000 1

2A

$ 8306.64 (8.3% yield) Investing $6000 for 4 years at 8.25% compounded quarterly yields the greater return.

17. $10,000, = 0.06, = 2, =3A r n t

2 3 60.062

10,000 10,000$8374.85

(1.03)1P

18. = $12,000, = 0.07, = 2, = 4A r n t

2 4 80.072

12,000 12,000$9112.94

1.0351P

19. = $10,000, = 0.095, = 12, = 3A r n t

12 3 360.09512

10,000 10,000$7528.59

(1.00791667)1P

20. = $22,000, = 0.105, = 12, = 4A r n t

12 4 480.10512

22,000 22,000$14,481.47

(1.00875)1P



367

21. a. 4 1

0.045$10,000 1

4A

4$10,000(1.01125)

$10, 457.65

b. 1A P rt

10, 457.65 10,000 1 1

10, 457.65 10,000 10,000

457.65 10,000

457.65 10,000

10,000 10,000

0.046

4.6%

r

r

r

r

r

r

22. a. 4 1

0.065$12,000 1

4A

4$12,000(1.01625)

$12,799.22

b. 1A P rt

12,799.22 12,000 1 1

12,799.22 12,000 12,000

799.22 12,000

799.22 12,000

12,000 12,000

0.067

6.7%

r

r

r

r

r

r

23. 2

0.061 1 0.061 6.1%

2Y

24. 4

0.061 1 0.061 6.1%

4Y

25. 12

0.061 1 0.062 6.2%

12Y

26. 360

0.061 1 0.062 6.2%

360Y

27. 1000

0.061 1 0.062 6.2%

1000Y

28. 1000

0.061 1 0.062 6.2%

100,000Y

29. 12

0.081 1 0.0830 8.3%

12Y

10.0825

1 1 0.0825 8.25%1

Y

8% compounded monthly is better..

30. 12

0.051 1 0.0512 5.1%

12Y

40.0525

1 1 0.0535 5.4%4

Y

5.25% compounded quarterly is better.

31. 2

0.0551 1 0.0558 5.6%

2Y

3600.054

1 1 0.05548 5.5%360

Y

5.5% compounded semiannually is better.

32. 1

0.071 1 0.07 7%

1Y

3600.0685

1 1 0.07089 7.1%360

Y

6.85% compounded daily is better.

33. (1 )

3 (1 0.05)

3 (1.05)

22.5 years

t

t

t

A P r

P P

t

34. (1 )

3 (1 0.10)

3 (1.10)

11.5 years

t

t

t

A P r

P P

t

35. (1 )

1.5 (1 0.10)

1.5 (1.10)

4.3 years

t

t

t

A P r

P P

t



368

36. (1 )

1.5 (1 0.05)

1.5 (1.05)

8.3 years

t

t

t

A P r

P P

t

37. (1 )

1.9 (1 0.08)

1.9 (1.08)

8.3 years

t

t

t

A P r

P P

t

38. (1 )

1.9 (1 0.12)

1.9 (1.12)

5.7 years

t

t

t

A P r

P P

t

39. 2 21

0.061 12,000 1 $41,528

2

ntr

A Pn

40. 2 21

0.051 10,000 1 $28,210

2

ntr

A Pn

41. a. 11

12 1

0.041 2600 1 $2704

1

0.051 2200 1 $2312.56

12

nt

nt

rA P

n

rA P

n

You will have $2704 $2312.56 $391.44 or approximately $391 more.

b. 1 5

12 5

0.041 2600 1 $3163.30

1

0.051 2200 1 $2823.39

12

nt

nt

rA P

n

rA P

n

You will have $3163.30 $2823.39 $339.91 or approximately $340 more.

c. 1 20

12 20

0.041 2600 1 $5696.92

1

0.051 2200 1 $5967.81

12

nt

nt

rA P

n

rA P

n

Your friend will have $5967.81 $5696.92 $270.89 or approximately $271 more.



369

42. a. 11

12 1

0.0351 3000 1 $3105

1

0.0481 2500 1 $2622.68

12

nt

nt

rA P

n

rA P

n

You will have $3105 $2622.68 $482.32 or approximately $482 more.

b. 1 5

12 5

0.0351 3000 1 $3563.06

1

0.0481 2500 1 $3176.60

12

nt

nt

rA P

n

rA P

n

You will have $3563.06 $3176.60 $386.46 or approximately $386 more.

c. 1 20

12 20

0.0351 3000 1 $5969.37

1

0.0481 2500 1 $6516.75

12

nt

nt

rA P

n

rA P

n

Your friend will have $6516.75 $5969.37 $547.38 or approximately $547 more.

43. 2 10

4 6

0.071 3000 1 $5969.37

2

0.07251 5969.37 1 $9186.60

4

nt

nt

rA P

n

rA P

n

The value of the account will be approximately $9187.

44. 2 10

4 8

0.05251 6000 1 $10,074.29

2

0.0541 10,074.29 1 $15,473.01

4

nt

nt

rA P

n

rA P

n

The value of the account will be approximately $15,473.

45. a. 12 384

0.0524 1 $5,027,400,000

12A

b. 360 384

0.0524 1 $5,225,000,000

360A

46. 1nt

rA P

n

360 212

76,320

0.06$450,000 1

360

$450,000(1.00016667)

$150,306,600,000

A



370

47. 360 1

2000 0.06 1 $120

0.0591 2000 1 $2122

360

$2122 2000 $122

nt

I Prt

rA P

n

I

The account that pays 5.9% compounded daily earns $122 $120 $2 more interest.

48. 360 1

1000 0.07 1 $70

0.0691 1000 1 $1071

360

$1071 1000 $71

nt

I Prt

rA P

n

I

The account that pays 6.9% compounded daily earns $71 $70 $1 more interest.

49. For compound interest once per year, use the formula 5000 1 0.055 .t

A

For compound interest continuously, use the formula 0.0555000 .tA e

Once a Year Once a Year Continous Continous

Years Amount Interest Amount Interest

1 $5275 $275 $5283 $283

5 $6535 $1535 $6583 $1583

10 $8541 $3541 $8666 $3666

20 $14,589 $9589 $15,021 $10,021

50. For compound interest once per year, use the formula 10,000 1 0.065 .t

A

For compound interest continuously, use the formula 0.06510,000 .tA e

Once a Year Once a Year Continous Continous

Years Amount Interest Amount Interest

1 $10,650 $650 $10,672 $672

5 $13,701 $3701 $13,840 $3840

10 $18,771 $8771 $19,155 $9155

20 $35,236 $25,236 $36,693 $26,693

51.

1nt

AP

r

n

2 13 26

$80,000, 0.06, 2, 13

80,000 80,000$37,096

(1.03)0.061

2

A r n t

P



371

52.

1nt

AP

r

n

$500,000, 0.07, 12, 65 30 35A r n t

12 35

500,000$43, 456

0.071

12

P

53. 115

360 15

75,000$38,755

0.0451 1

1

75,000$41,163

0.041 1

360

nt

nt

AP

r

n

AP

r

n

54. 1 20

360 20

150,000$51,410

0.0551 1

1

150,000$55,186

0.051 1

360

nt

nt

AP

r

n

AP

r

n

55. 360

0.0541 1 1 1 0.0555 5.55%

360

nr

Yn

56. 360

0.03751 1 1 1 0.0382 3.82%

360

nr

Yn

57. 4

12

360

0.0421 1 1 1 0.043 4.3%

4

0.0421 1 1 1 0.043 4.3%

12

0.0421 1 1 1 0.043 4.3%

360

n

n

n

rY

n

rY

n

rY

n

As the number of compounding periods increases, the effective annual yield increases slightly. However, with the rates rounded to the nearest tenth of a percent, this increase is not evident.



372

58. 4

12

360

0.0461 1 1 1 0.047 4.7%

4

0.0461 1 1 1 0.047 4.7%

12

0.0461 1 1 1 0.047 4.7%

360

n

n

n

rY

n

rY

n

rY

n

As the number of compounding periods increases, the effective annual yield increases slightly. However, with the rates rounded to the nearest tenth of a percent, this increase is not evident.

59. 2

360

0.0451 1 1 1 0.0455 4.55%

2

0.0441 1 1 1 0.0450 4.50%

360

n

n

rY

n

rY

n

The account paying 4.5% compounded semiannually is the better investment.

60. 2

360

0.0491 1 1 1 0.0496 4.96%

2

0.0481 1 1 1 0.0492 4.92%

360

n

n

rY

n

rY

n

The account paying 4.9% compounded semiannually is the better investment.

65. does not make sense; Explanations will vary. Sample explanation: At the same rate, any compounding period will be a better deal than simple interest.

66. does not make sense; Explanations will vary. Sample explanation: The best deal can not be determined without knowing the compounding period as well.

67. does not make sense; Explanations will vary. Sample explanation: Compounding continuously does not result in an infinite amount of money.

68. makes sense

69. 1nt

rA P

n

Have $6000 in the account for 6 years: 2 6

0.05$6000 1 $8069.33

2A

Have $4000 in the account for 4 years: 2 4

0.05$4000 1 $4873.61

2A

Balance after 6 years $8069.33 $4873.61

$12,942.94



373

70. 1nt

rA P

n

Start with $5000 in account for 2 years: 12 2

0.08$5000 1 $5864.44

12A

Then withdraw $1500, which leaves $5864.44 – $1500 = $4364.44

Leave $4364.44 in the account for 1 year: 12 1

0.08$4364.44 1 $4726.69

12A

Then add $2000, so now have $4726.69 + $2000 = $6726.69

Have $6726.69 in account for 3 years: 12 3

0.086726.69 1 $8544.49

12A

71. Substitute Y for r in 1A P rt

Thus, 1A P Yt

Substitute 1P Yt for A in 1nt

rA P

n

and substitute 1 for t.

1

1 1

11 1

1 1

1 1

nt

n

n

n

rP Yt P

n

rPP Y n

P P

rY

n

rY

n

Check Points 8.4

1. a. Value at end of year 1 $2000 Value at end of year 2 $2000(1 0.10) $2000 $4200

Value at end of year 3 $4200(1 0.10) $2000 $6620

b. $6620 $2000 3 $620

2. a.

40

(1 ) 1

3000 (1 0.08) 1

0.08$777,170

tP rA

r

A

b. $777,170 40 $3000 $657,170



374

3. a.

12 350.09512

0.09512

1 1

100 1 1

$333,946

ntrn

rn

PA

A

b. $333,946 $100 12 35 $291,946

4. a.

0.0912

12 180.0912

1 1

100,000

1 1

$187

rn

ntrn

AP

P

b. Deposits: $187 18 12 $40,392 Interest: $100,000 $40,392 $59,608

5. a. High price = $63.38, Low price = $42.37

b. Dividend = $0.72 3000 = $2160

c. Annual return for dividends alone = 1.5% 1.5% is much lower than the 3.5% bank rate.

d. Shares traded = 72,032 100 7, 203,200 shares

e. High price = $49.94, Low price = $48.33

f. Price at close = $49.50

g. The price went up $0.03 per share.

h. $49.50

Annual earnings per share $1.3437

Exercise Set 8.4

1. a.

20

(1 ) 1

2000 (1 0.05) 1

0.05$66,132

tP rA

r

A

b. $66,132 20 $2000 $26,132

2. a.

20

(1 ) 1

3000 (1 0.04) 1

0.04$89,334

tP rA

r

A

b. $89,334 20 $3000 $29,334

3. a.

40

(1 ) 1

4000 (1 0.065) 1

0.065$702,528

tP rA

r

A

b. $702,528 40 $4000 $542,528

4. a.

40

(1 ) 1

4000 (1 0.055) 1

0.055$546,422

tP rA

r

A

b. $546,422 40 $4000 $386,422

5. a.

12 300.0612

0.0612

1 1

50 1 1

$50, 226

ntrn

rn

PA

A

b. $50, 226 $50 12 30 $32,226



375

6. a.

12 300.0512

0.0512

1 1

60 1 1

$49,936

ntrn

rn

PA

A

b. $49,936 $60 12 30 $28,336

7. a.

2 250.0452

0.0452

1 1

100 1 1

$9076

ntrn

rn

PA

A

b. $9076 $100 2 25 $4076

8. a.

2 250.0652

0.0652

1 1

150 1 1

$18,225

ntrn

rn

PA

A

b. $18,225 $150 2 25 $10,725

9. a.

4 60.06254

0.06254

1 1

1000 1 1

$28,850

ntrn

rn

PA

A

b. $28,850 $1000 4 6 $4850

10. a.

4 60.03254

0.03254

1 1

1200 1 1

$31,658

ntrn

rn

PA

A

b. $31,658 $1200 4 6 $2858

11. a.

0.06

1

1 180.061

1 1

140,000

1 1

$4530

rn

ntrn

AP

P

b. Deposits: $4530 1 18 $81,540

Interest: $140,000 $81,540 $58,460

12. a.

0.05

1

1 180.051

1 1

150,000

1 1

$5332

rn

ntrn

AP

P

b. Deposits: $5332 1 18 $95,976

Interest: $150,000 $95,976 $54,024

13. a.

0.045

12

12 100.04512

1 1

200,000

1 1

$1323

rn

ntrn

AP

P


14. a.

0.075

12

12 100.07512

1 1

250,000

1 1

$1406

rn

ntrn

AP

P




376

15. a.

0.0725

12

12 400.072512

1 1

1,000,000

1 1

$356

rn

ntrn

AP

P

b. Deposits: $356 12 40 $170,880 Interest: $1,000,000 $170,880 $829,120

16. a.

0.0825

12

12 400.082512

1 1

1,500,000

1 1

$400

rn

ntrn

AP

P

b. Deposits: $400 12 40 $192,000

Interest: $1,500,000 $192,000 $1,308,000

17. a.

0.035

4

4 50.0354

1 1

20,000

1 1

$920

rn

ntrn

AP

P

b. Deposits: $920 4 5 $18,400 Interest: $20,000 $18, 400 $1600

18. a.

0.045

4

4 50.0454

1 1

25,000

1 1

$1122

rn

ntrn

AP

P

b. Deposits: $1122 4 5 $22,440

Interest: $25,000 $22, 440 $2560


b. Dividend = $1.20 700 $840

c. Annual return for dividends alone = 2.2% 2.2% is lower than a 3% bank rate.

d. Shares traded = 5915 100 591,500 shares


f. Price at close = $55.50

g. The price went up $1.25 per share.

h. $55.50

Annual earnings per share17

$3.26


b. Dividend = $2.18 700 $1526

c. Annual return for dividends alone = 4.7% 4.7% is higher than a 3% bank rate.

d. Shares traded = 7473 100 747,300 shares


f. Price at close $46.88

g. The price went down $1.31 per share

h. Annual earnings per share

= $46.88

$2.1322

21. a. Lump-Sum Deposit:

20

(1 )

30,000(1 0.05)

$79,599

tA P r

A

Periodic Deposit:

20

(1 ) 1

1500 (1 0.05) 1

0.05$49,599

tP rA

r

A

The lump-sum investment will have $79,599 $49,599 $30,000 more.

b. Lump-Sum Interest: $79,599 $30,000 $49,599 Periodic Deposit Interest: $49,599 $30,000 $19,599 The lump-sum investment will have $49,599 $19,599 $30,000 more.



377

22. a. Lump-Sum Deposit:

25

(1 )

40,000(1 0.065)

$193,108

tA P r

A

Periodic Deposit:

25

(1 ) 1

1600 (1 0.065) 1

0.065$94,220

tP rA

r

A

The lump-sum investment will have $193,108 $94,220 $98,888 more.

b. Lump-Sum Interest: $193,108 $40,000 $153,108 Periodic Deposit Interest: $94, 220 $40,000 $54,220 The lump-sum investment will have $153,108 $54,220 $98,888 more.

23. a.

0.0812

12 400.0812

1 1

1,000,000

1 1

$287

rn

ntrn

AP

P

b. Adjusted gross income with IRA: Adj. gross income $50,000 $287 12

$46,556

Taxable income with IRA: Taxable inc $46,556 ($3200 $5000)

$38,356

Income tax with IRA: 0.10(7300) 0.15(29,700 7300)

0.25(38,356 29,700)

$6254

Adjusted gross income without IRA: Adj. gross income $50,000 $0

$50,000

Taxable income without IRA: Taxable inc $50,000 ($3200 $5000)

$41,800

Income tax without IRA: 0.10(7300) 0.15(29,700 7300)

0.25(41,800 29,700)

$7115

c. Percent of gross income with IRA: 6254

12.5%50,000

Percent of gross income without IRA: 7115

14.2%50,000

24. a.

0.0712

12 400.0712

1 1

650,000

1 1

$248

rn

ntrn

AP

P

b. Adjusted gross income with IRA: Adj. gross income $50,000 $248 12

$47,024

Taxable income with IRA: Taxable inc $47,024 ($3200 $5000)

$38,824

Income tax with IRA: 0.10(7300) 0.15(29,700 7300)

0.25(38,824 29,700)

$6371

Adjusted gross income without IRA: Adj. gross income $50,000 $0

$50,000

Taxable income without IRA: Taxable inc $50,000 ($3200 $5000)

$41,800

Income tax without IRA: 0.10(7300) 0.15(29,700 7300)

0.25(41,800 29,700)

$7115

c. Percent of gross income with IRA: 6371

12.7%50,000

Percent of gross income without IRA: 7115

14.2%50,000



378

25. (1 ) 1tP r

Ar

(1 ) 1

(1 ) 1

(1 ) 1 (1 ) 1

(1 ) 1

(1 ) 1

t

t

t t

t

t

Ar P r

P rAr

r r

ArP

r

ArP

r

This formula describes the deposit necessary at the end of each year that yields A dollars after t years with interest rate r compounded annually.

26. 1 1

ntrn

rn

PA

1 1

1 1

1 1 1 1

1 1

1 1

ntr rn n

ntrr nn

nt ntr rn n

rnntr

n

rnntr

n

A P

PA

AP

AP

This formula describes the deposit necessary at the end of each compounding period that yields A dollars after t years with interest rate r and n compounding periods per year.

27. a.

5

(1 ) 1

2000 (1 0.075) 1

0.075$11,617

tP rA

r

A

b. $11,617 5 $2000 $1617

28. a.

5

(1 ) 1

2500 (1 0.0625) 1

0.0625$14,163

tP rA

r

A

b. $14,163 5 $2500 $1663

29. a.

12 400.05512

0.05512

1 1

50 1 1

$87,052

ntrn

rn

PA

A

b. $87,052 $50 12 40 $63,052

30. a.

12 400.06512

0.06512

1 1

75 1 1

$171, 271

ntrn

rn

PA

A

b. $171,271 $75 12 40 $135, 271

31. a.

4 100.1054

0.1054

1 1

10,000 1 1

$693,031

ntrn

rn

PA

A

b. $693,031 $10,000 4 10 $293,031

32. a.

4 100.094

0.094

1 1

15,000 1 1

$956,793

ntrn

rn

PA

A

b. $956,793 $15,000 4 10 $356,793



379

33. a.

0.05

2

2 40.052

1 1

3500

1 1

$401

rn

ntrn

AP

P

b. Deposits: $401 2 4 $3208 Interest: $3500 $3208 $292

34. a.

0.07

2

2 40.072

1 1

4000

1 1

$442

rn

trn

AP

P

b. Deposits: $442 2 4 $3536 Interest: $4000 $3536 $464

35.

0.065

12

12 450.06512

1 1

2,000,000

1 1

$620

rn

ntrn

AP

P

You must invest $620 per month. Amount from interest: $2,000,000 $620 12 45 $1,665,200

36.

0.085

12

12 450.08512

1 1

4,000,000

1 1

$641

rn

ntrn

AP

P

You must invest $641 per month. Amount from interest: $4,000,000 $641 12 45 $3,653,860

50. does not make sense; Explanations will vary. Sample explanation: An annuity is the same as a lump-sum deposit.



380

51. does not make sense; Explanations will vary. Sample explanation: At the end of 30 years you will only have:

12 300.03512

0.03512

1 1 20 1 1$12,708.25.

ntrn

rn

PA

52. makes sense

53. does not make sense; Explanations will vary. Sample explanation: With stocks it is possible to lose part or all of your investment.

54. Use the simple interest formula to find the principal necessary to earn $60,000 per year.

60,000 0.08 1

60,000

0.08750,000

I = Prt

= P

P

P

Next, find the necessary monthly deposit that will result a principal of $750,000 after 30 years.

0.0812

12 300.0812

1 1

750,000

1 1

$504

rn

ntrn

AP

P

Check Points 8.5

1. a.

0.075

1212 150.075

12

175,500$1627

1 1 1 1

rn

ntrn

PPMT

b. $1627 12 15 $175,500 $117,360

c. $266,220 $117,360 $148,860

2. Interest for first month = 1

$200,000 0.07 $1166.6712

Prt

Principle payment = $1550.00 $1166.67 $383.33 Balance of loan = $200,000 $383.33 $199,616.67

Interest for second month = 1

$199,616.67 0.07 $1164.4312

Prt

Principle payment = $1550.00 $1164.43 $385.57 Balance of loan = $199,616.67 $385.57 $199,231.10

Payment Number

Interest Payment

Principal Payment

Balance of Loan

1 $1166.67 $383.33 $199,616.67

2 $1164.43 $385.57 $199,231.10



381

3. a.

0.0812

12(4)0.0812

15,000$366

1 1 1 1

rn

ntrn

PPMT

Total interest for loan A: $367 12 4 $15,000 $2616

b.

0.1012

12(6)0.1012

15,000$278

1 1 1 1

rn

ntrn

PPMT

Total interest for loan A: $278 12 6 $15,000 $5016

c. Monthly payments are less with the longer-term loan, but there is more interest with the longer-term loan.

4. a. Make a table that shows the unpaid balance for each transaction date, the number of days at each unpaid balance, and then multiply each unpaid balance by the number of days that the balance was outstanding.

Number of Days Unpaid NumberDate Unpaid Balance

at Each Unpaid Balance Balance of Days

May 1 $8240.00 6 $49,440.00

May 7 $8240.00 $350.00 $7890.00 8 $63,120.00

May 15 $7890.00 $1405.00 $9295.00 2 $18,590.0

0

May 17 $9295.00 $45.20 $9340.20 13 $121,422.60

May 30 $9340.20 $180.72 $9520.92 2 $19,041.84

Total days: 31 Total: $271,614.44

Sum of unpaid balancesAverage daily balance

Number of days in the billing period

$271,614.44

31$8,761.76

b. Pr

($8761.76)(0.016)(1)

$140.19

I t

c. Balance due $9520.92 $140.19 $9661.11

d. Because the balance exceeds $360, the minimum payment is 1

36 of the balance due.

Minimum Payment$9661.11

$26936



382

Exercise Set 8.5

1. a. $220,000(0.20) $44,000

b. $220,000 $44,000 $176,000

c. $176,000(0.03) $5280

d.

0.071212(30)0.07

12

176,000$1171

1 1 1 1

rn

ntrn

PPMT

e. $1171(12)(30) $176,000 $245,560

2. a. $180,000(0.05) $9000

b. $180,000 $9,000 $171,000

c. $171,000(0.01) $1710

d.

0.081212(30)0.08

12

171,000$1255

1 1 1 1

rn

ntrn

PPMT

e. $1255(12)(30) $171,000 $280,800

3. Mortgage amount: $100,000 $100,000(0.05) $95,000

Payment for 20-year loan:

0.0812

12(20)0.0812

95,000$795

1 1 1 1

rn

ntrn

PPMT

Interest for 20-year loan: $795(12)(20) $100,000 $90,800


0.0812

12(30)0.0812

95,000$697

1 1 1 1

rn

ntrn

PPMT


The buyer saves $150,920 $90,800 $60,120

4. Mortgage amount: $160,000 $160,000(0.15) $136,000


0.081212(15)0.08

12

136,000$1300

1 1 1 1

rn

ntrn

PPMT



0.081212(30)0.08

12

136,000$998

1 1 1 1

rn

ntrn

PPMT


The buyer saves $199,280 $74,000 $125,280



383

5. Payment for 30-year 8% loan:

0.081212(30)0.08

12

150,000$1101

1 1 1 1

rn

ntrn

PPMT


Payment for 20-year 7.5% loan:

0.075

1212(20)0.075

12

150,000$1208

1 1 1 1

rn

ntrn

PPMT


The 20-year 7.5% loan is more economical. The buyer saves $246,360 139,920 $106,440

6. Payment for 30-year 8% loan:

0.0812

12(30)0.0812

90,000$660

1 1 1 1

rn

ntrn

PPMT


Payment for 15-year 7.5% loan:

0.075

1212(15)0.075

12

90,000$834

1 1 1 1

rn

ntrn

PPMT


The 15-year 7.5% loan is more economical. The buyer saves $147,600 $60,120 $87,480

7. Payment for Mortgage A:

0.071212(30)0.07

12

120,000$798

1 1 1 1

rn

ntrn

PPMT

Interest for Mortgage A: $798(12)(30) $120,000 $167,280

Points for Mortgage A: $120,000(0.01) $1200

Cost for Mortgage A: $2000 $1200 $167, 280 $170,480

Payment for Mortgage B:

0.065

1212(30)0.065

12

120,000$758

1 1 1 1

rn

ntrn

PPMT

Interest for Mortgage B: $758(12)(30) $120,000 $152,880

Points for Mortgage B: $120,000(0.04) $4800

Cost for Mortgage B: $1500 $4800 $152,880 $159,180 Mortgage A has the greater cost by $170,480 $159,180 $11,300

8. Payment for Mortgage A:

0.0725

1212(30)0.0725

12

250,000$1705

1 1 1 1

rn

ntrn

PPMT

Interest for Mortgage A: $1705(12)(30) $250,000 $363,800

Points for Mortgage A: $250,000(0.01) $2500

Cost for Mortgage A: $2000 $2500 $363,800 $368,300


0.0625

1212(30)0.0625

12

250,000$1539

1 1 1 1

rn

ntrn

PPMT


Points for Mortgage B: $250,000(0.04) $10,000

Cost for Mortgage B: $350 $10,000 $304,040 $314,390

Mortgage A has the greater cost by $368,300 $314,390 $53,910.



384

9. a.

0.1812

12(2)0.1812

4200$210

1 1 1 1

rn

ntrn

PPMT

b. $210(12)(2) $4200 $840

10. a.

0.165

1212(2)0.165

12

3600$178

1 1 1 1

rn

ntrn

PPMT

b. $178(12)(2) $3600 $672

11. a.

0.105

1212(3)0.105

12

4200$137;

1 1 1 1

rn

ntrn

PPMT

This payment is lower.

b. $137(12)(3) $4200 $732; This loan has less interest.

12. a.

0.095

1212(3)0.095

12

3600$116;

1 1 1 1

rn

ntrn

PPMT

This payment is lower.

b. $116(12)(3) $3600 $576; This loan has less interest.

13.

0.1812

12(1)0.1812

4200$386

1 1 1 1

rn

ntrn

PPMT

Total interest: $386(12)(1) $4200 $432

Additional each month: $386 $210 $176 Less total interest: $840 $432 $408

14.

0.165

1212(1)0.165

12

3600$328

1 1 1 1

rn

ntrn

PPMT

Total interest: $328(12)(1) $3600 $336

Additional each month: $328 $178 $150 Less total interest: $672 $336 $336

15. a.

0.0812

12(4)0.0812

10,000$244.13

1 1 1 1

rn

ntrn

PPMT

Total interest: $244.13(12)(4) $10,000 $1718.24

b. Payment Number

Interest

Principal

Loan Balance

1 1

1210,000(0.08)

$66.67

244.13 66.67

$177.46

10,000 177.46

$9822.54

2 1

129822.54(0.08)

$65.48

244.13 65.48

$178.65

9822.54 178.65

$9643.89

3 1

129643.89(0.08)

$64.29

244.13 64.29

$179.84

9643.89 179.84

$9464.05



385

16. a.

0.0812

12(4)0.0812

30,000$732.39

1 1 1 1

rn

ntrn

PPMT

Total interest: $732.39(12)(4) $30,000 $5154.72

b. Payment Number

Interest

Principal

Loan Balance

1 1

1230,000(0.08)

$200.00

732.39 200.00

$532.39

30,000 532.39

$29,467.61

2 1

1229, 467.61(0.08)

$196.45

732.39 196.45

$535.94

29, 467.61 535.94

$28,931.67

3 1

1228,931.67(0.08)

$192.88

732.39 192.88

$539.51

28,931.67 539.51

$28,392.16

17. a.

0.085

1212(20)0.085

12

40,000$347.13

1 1 1 1

rn

ntrn

PPMT

Total interest: $347.13(12)(20) $40,000 $43,311.20

b. Payment Number

Interest

Principal

Loan Balance

1 1

1240,000(0.085)

$283.33

347.13 283.33

$63.80

40,000 63.80

$39,936.20

2 1

1239,936.20(0.085)

$282.88

347.13 282.88

$64.25

39,936.20 64.25

$39,871.95

3 1

1239,871.95(0.085)

$282.43

347.13 282.43

$64.70

39,871.95 64.70

$39,807.25

c.

0.085

1212(10)0.085

12

40,000$495.94

1 1 1 1

rn

ntrn

PPMT

Amount by which the monthly payment for the 10-year loan is greater: $495.94 $347.13 $148.81 Total interest for 10-year loan: $495.94(12)(10) $40,000 $19,512.80

Savings from 10-year loan: $43,311.20 $19,512.80 $23,798.40



386

18. a.

0.075

1212(20)0.075

12

50,000$402.80

1 1 1 1

rn

ntrn

PPMT

Total interest: $402.80(12)(20) $50,000 $46,672

b. Payment Number

Interest

Principal

Loan Balance

1 1

1250,000(0.075)

$312.50

402.80 312.50

$90.30

50,000 90.30

$49,909.70

2 1

1249,909.70(0.075)

$311.94

402.80 311.94

$90.86

49,909.70 90.86

$49,818.84

3 1

1249,818.84(0.075)

$311.37

402.80 311.37

$91.43

49,818.84 91.43

$49,727.41

c.

0.075

1212(10)0.075

12

50,000$593.51

1 1 1 1

rn

ntrn

PPMT

Amount by which the monthly payment for the 10-year loan is greater: $593.51 $402.80 $190.71 Total interest for 10-year loan: $593.51(12)(10) $50,000 $21,221.20

Savings from 10-year loan: $46,672 $21, 221.20 $25,450.80 19. a. Make a table that shows the unpaid balance for each transaction date, the number of days at each unpaid balance,

and then multiply each unpaid balance by the number of days that the balance was outstanding.



March 1 $6240.00 4 $24,960.00

March 5 $6240.00 $300.00 $5940.00 2 $11,880.00

March 7 $5940.00 $40.00 $5980.00 5 $29,90

0.00

March 12 $5980.00 $90.00 $6070.00 9 $54,630.00

March 21 $6070.00 $230.00 $6300.00 11 $69,300.00




$190,670.00

31$6150.65

b. Pr

($6150.65)(0.015)(1)

$92.26

I t

c. Balance due $6300.00 $92.26 $6392.26




$17836



387




March 1 $7150.00 3 $21,450.00

March 5 $7150.00 $400.00 $6750.00 2 $13,500.00

March 7 $6750.00 $1200.00 $7950.00 9 $71,

550.00

March 12 $7950.00 $40.00 $7990.00 15 $119,850.00

March 21 $7990.00 $50.00 $8040.00 2 $16,080.00




$242,430.00

31$7820.32

b. Pr

($7820.32)(0.015)(1)

$117.30

I t

c. Balance due $8040.00 $117.30 $8157.30




$22736




June 1 $2653.48 5 $13,267.40

June 6 $2653.48 $1000.00 $1653.48 2 $3306.96

June 8 $1653.48 $36.25 $1689.73 1 $1689.73

Ju

ne 9 $1689.73 $138.43 $1828.16 8 $14,625.28

June 17 $1828.16 $42.36 $127.19 $1997.71 10 $19,977.10

June 27 $1997.71 $214.83 $2212.54 4 $8850.16




$61,716.63

30$2057.22



388

b. Pr

($2057.22)(0.012)(1)

$24.69

I t

c. Balance due $2212.54 $24.69 $2237.23




$9025




June 1 $4037.93 4 $16,151.72

June 5 $4037.93 $350.00 $3687.93 5 $18,439.65

June 10 $3687.93 $31.17 $3719.10 5 $18,595.

50

June 15 $3719.10 $42.50 $3761.60 7 $26,331.20

June 22 $3761.60 $43.86 $112.91 $3918.37 7 $27,428.59

June 29 $3918.37 $96.73 $4015.10 2 $8030.20




$114,976.86

30$3832.56

b. Pr

($3832.56)(0.012)(1)

$45.99

I t

c. Balance due $4015.10 $45.99 $4061.09




$16325

33. does not make sense; Explanations will vary. Sample explanation: The 3.5% rate will not eliminate paying more on interest than on the principal.

34. does not make sense; Explanations will vary. Sample explanation: The payments could still be larger with the 3-year loan.

35. does not make sense; Explanations will vary. Sample explanation: Paying the minimum payment will cost more money in interest over the long run.

36. does not make sense; Explanations will vary. Sample explanation: The given formula is for fixed installment loans not credit card payments.



389

37. 1 1

1

ntrnntr

n rn

PMTP

1 1 1

1 11

1 1 1 1

1

1 1

1

1

1 1

1

1 1

1 1

1 1

nt ntr r rn n n

ntnt rr r nn nnt ntr r

n n

ntr rn n

ntrn

ntr rn n

ntrnntr

nntr

n

rn

ntrn

nt ntr rn n

rn

ntrn

P PMT

PMTP

PPMT

P

PMT

PPMT

PPMT

38. a. Begin with

PMT PV1 1

rn

ntrn

Next multiply both sides by 1 1

ntrn

rn

which gives:

1 1 1 1

PMT PV1 1

nt ntr rrn nn

r nt rrn nn

Canceling produces: 1 1

PMT PV

ntrn

rn

Finally, interchange the sides: 1 1

PV PMT

ntrn

rn

b. 12 200.063

120.063

12

1 1 1 1PV PMT 1002.74 $136,641.85

ntrn

rn



390

Chapter 8 Review Exercises

1. 4

4 5 0.80 80%5

2. 1

1 8 0.125 12.5%8

3. 3

3 4 0.75 75%4

4. 0.72 = 72%

5. 0.0035 = 0.35%

6. 4.756 = 475.6%

7. 65% = 0.65

8. 99.7% = 0.997

9. 150% = 1.50

10. 3% = 0.03

11. 0.65% = 0.0065

12. 14 % 0.25% 0.0025

13. A PB 0.08 120

9.6

A

A

14. a. Tax = 0.06($24) = $1.44

b. Total cost = $24 + $1.44 = $25.44

15. a. Amount of discount = 0.35($850) = $297.50

b. Sale price = $850 – $297.50 = $552.50


$37,500

Step 2. Determine the taxable income. Since the total deduction of $8300 is greater than the standard deduction of $5450, use $8300. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $37,500 ($3500 $8300)

$25,700


0.10(8025) 0.15(25,700 8025)

$3453.75


$3453.75

17. 45 40

0.125 12.5%40

increase.

18. $56.00 $36.40

0.35 35%$56.00

decrease.

19. The statement is not true. The 10% loss is $1000.

0.10 10,000 1000

This leaves $9000. The 10% rise is $900.

0.10 9,000 900

Thus there is $9900 in the portfolio. Find the percent of decrease: amount of decrease 100

0.01 1%original amount 10,000

The net loss of $100 is a 1% decrease from the original.

20. I = Prt = ($6000)(0.03)(1) = $180

21. I = Prt = ($8400)(0.05)(6) = $2520

22. 9

($20,000)(0.08) $120012

I Prt

23. 60

($36,000)(0.15) $900360

I Prt


ISM: Thinking Mathematically Chapter 8 Review Exercises

391

24. a. I Prt 4($3500)(0.105)

12

$122.50

b. Maturity value $3500 $122.50

$3622.50

25. (1 )A P rt 9

1212,000(1 0.082 )

$12,738

A

A

26. (1 )A P rt

5750 5000 1 2

5750 5000 10,000

750 10,000

0.075

7.5%

r

r

r

r

r

27. (1 )A P rt

16,000 1 (0.065)(3)

16,000 1.195

13,389.12

$13,389.12

P

P

P

P

28. (1 )A P rt

12,000 1 (0.073)(4)

12,000 1.292

9287.93

$9287.93

P

P

P

P

29. (1 )A P rt

121800 1500 1

1800 1500 750

300 750

0.4

40%

r

r

r

r

r

30. a. 9121800 0.07 $94.50I Prt

b. Amount received: $1800 $94.50 $1705.50

c. I Prt

91294.50 1705.50

94.50 1279.125

0.0739

7.4%

r

r

r

r

31. a. 5

5

$7000(1 0.03)

$7000(1.03)

$8114.92

A

b. Interest = $8114.92 – $7000 = $1114.92

32. a. 4 10

40

0.025$30,000 1

4

$30,000(1.00625)

$38,490.80

A

b. Interest = $38,490.80 – $30,000 = $8490.80

33. a. 12 20

240

0.04$2500 1

12

$2500(1.003333)

$5556.46

A

b. Interest = $5556.46 – $2500 = $3056.46

34. 12(10)0.07

12

1

14,000 1

$28,135

ntrnA P

A

0.0685(10)14,000

$27,773

rtA Pe

A e

The 7% compounded monthly is the better investment by $28,135 $27,773 $362.

35. 12 18

100,000$28,469.44

0.071

12

P

36. 4 35

75,000$13,175.19

0.051

4

P



392

37. a. 4 1

0.06$2000 1

4A

4$2000(1.015)

$2122.73

b. 1A P rt

2122.73 2000 1 1

2122.73 2000 2000

122.73 2000

0.061365

6.1%

r

r

r

r

r

38. 4

0.0551 1 0.0561 5.6%

4Y

5.5% compounded quarterly is equivalent to 5.6% compounded annually.

39. 6.25% compounded monthly: 12

0.06251 1 0.0643 6.4%

12Y

6.3% compounded annually: 1

0.0631 1 0.063 6.3%

1Y

6.25% compounded monthly is better than 6.3% compounded annually.

40. a.

20

(1 ) 1

520 (1 0.06) 1

0.06$19,129

tP rA

r

A

b. $19,129 20 $520 $8729

41. a.

12(30)0.05512

0.05512

1 1

100 1 1

$91,361

ntrn

rn

PA

A

b. $91,361 30 12 $100 $55,361

42. a.

0.0725

4

4(5)0.07254

1 1

25,000

1 1

$1049

rn

ntrn

AP

P

b. Deposits: 5 4 $1049 $20,980

Interest: $25,000 $20,980 $4020

43. High = $64.06, Low = $26.13

44. Dividend = $0.16(900) = $144

45. Annual return for dividends alone = 0.3%

46. Shares traded yesterday = 5458 · 100 = 545,800 shares

47. High = $61.25, Low = $59.25

48. Price at close = $61

49. Change in price = $1.75 increase

50. Annual earnings per share$61

$1.4941

52. a. $240,000(0.20) $48,000

b. $240,000 $48,000 $192,000

c. $192,000(0.02) $3840

d.

0.071212(30)0.07

12

1 1

192,000

1 1

$1277

rn

ntrn

PPMT

e. $1277(12)(30) $192,000 $267,720


ISM: Thinking Mathematically Chapter 8 Review Exercises

393

53. Payment for 30-year mortgage:

0.08512

12(30)0.08512

70,000$538

1 1 1 1

rn

ntrn

PPMT

Interest for 30-year mortgage: $538(12)(30) $70,000 $123,680

Payment for 20-year mortgage:

0.081212(20)0.08

12

70,000$586

1 1 1 1

rn

ntrn

PPMT

Interest for 20-year mortgage: $586(12)(20) $70,000 $70,640

The 20-year mortgage saves $123,680 $70,640 $53,040.

An advantage of the 30-year loan is the lower monthly payment. A disadvantage of the 30-year loan is the greater total interest.

An advantage of the 20-year loan is the lower total interest. A disadvantage of the 20-year loan is the higher monthly payment.

54. a. Payment for Mortgage A:

0.0851212(30)0.085

12

100,000$769

1 1 1 1

rn

ntrn

PPMT


0.0751212(30)0.075

12

100,000$699

1 1 1 1

rn

ntrn

PPMT

b. Interest for Mortgage A: $769(12)(30) $100,000 $176,840

Cost for Mortgage A: $0 $0 $176,840 $176,840


Points for Mortgage B: $100,000(0.03) $3000

Cost for Mortgage B: $1300 $3000 $151,640 $155,940 Mortgage A has the greater cost by $176,840 $155,940 $20,900.

55. a. Payment for Loan A:

0.07212

12(3)0.07212

100,000$465

1 1 1 1

rn

ntrn

PPMT

Interest for Loan A: $465(12)(3) $15,000 $1740



394

b. Payment for Loan B:

0.08112

12(5)0.08112

100,000$305

1 1 1 1

rn

ntrn

PPMT

Interest for Loan B: $305(12)(5) $15,000 $3300

c. The longer term has a lower monthly payment but greater total interest.

56. a.

0.1812

12(2)0.1812

11,211$559.70

1 1 1 1

rn

ntrn

PPMT

b. Total interest: $559.70(12)(2) $11, 211 $2221.80

c. Payment Number

Interest

Principal

Loan Balance

1 1

1211,211(0.18)

$168.17

559.70 168.17

$391.53

11,211 391.53

$10,819.47

2 1

1210,819.47(0.18)

$162.29

559.70 162.29

$397.41

10,819.47 397.41

$10,422.06

3 1

1210, 422.06(0.18)

$156.33

559.70 156.33

$403.37

10, 422.06 403.37

$10,018.69

57. a. Make a table that shows the unpaid balance for each transaction date, the number of days at each unpaid balance,




November 1 $4620.80 6 $27,724.80

November 7 $4620.80 $650.00 $3970.80 4 $15,883.20

November 11 $3970.80 $350.25 $4,3

21.05 14 $60,494.70

November 25 $4321.05 $125.70 $4446.75 3 $13,340.25

November 28 $4446.75 $38.25 $4485.00 3 $13,455.00




$130,897.95

30$4363.27

b. Pr

($4363.27)(0.011)(1)

$48.00

I t

c. Balance due $4485.00 $48.00 $4533.00




$12636


ISM: Thinking Mathematically Chapter 8 Test

395

Chapter 8 Test

1. a. Discount = 0.15($120) = $18

b. Sale price = $120 – $18 = $102


$34,500

Step 2. Determine the taxable income. Since the total deduction of $6000 is greater than the standard deduction of $5000, use $6000. Taxable inc. = Adj. gross inc– (Exempt.+Deduct.) Taxable inc. $34,500 ($3500 $6000)

$25,000

Step 3. Determine the income tax. Tax Computation 0.10(8025) 0.15(25,000 8025)

$3348.75


$3348.75

3. 3500 2000

0.75 75% increase2000

4. (1 )A P rt

3122400 1 (0.12)

$2472

A

A

The future value is $2472. The interest earned is $72.

5. (1 )A P rt

3000 2000 1 (2)

3000 2000 4000

1000 4000

0.25

25%

r

r

r

r

r

6. (1 )A P rt

6127000 1 (0.09)

7000 1.045

6698.57

$6698.57

P

P

P

P



396

7. 4

0.0451 1 0.0458 4.58%

4Y

4.5% compounded quarterly is equivalent to 4.58% compounded annually.

8. a. 12(5)0.065

12

1

6000 1

$8297

ntrnA P

A

b. $8297 $6000 $2297

9. a.

12(5)0.06512

0.06512

1 1

100 1 1

$7067

ntrn

rn

PA

A

b. $7067 $6000 $1067

c. answers will vary

10.

2(4)0.0952

1

3000

1

$2070

ntrn

AP

P

11.

0.0625

12

12(40)0.062512

1 1

1,500,000

1 1

$704

rn

ntrn

AP

P

Interest $1,500,000 $704(12)(40)

$1,162,080

12. High = $25.75, Low = $25.50

13. Dividend = $2.03 · 1000 = $2030

14. Total price paid 600($25.75) $15,450

Broker’s commission 0.025($15,450) $386.25

15. Down payment = 0.10($120,000) = $12,000

16. Amount of mortgage = $120,000 – $12,000 = $108,000


ISM: Thinking Mathematically Chapter 8 Test

397

17. Two points = 0.02($108,000) = $2160

18.

0.085

1212(30)0.085

12

108,000$830

1 1 1 1

rn

ntrn

PPMT

19. Total cost of interest = 360($830) – $108,000 = $190,800

20. a.

0.068

1212(10)0.068

12

20,000$230

1 1 1 1

rn

ntrn

PPMT

Total interest: $230(12)(10) $20,000 $7600

b. Payment Number

Interest

Principal

Loan Balance

1 1

1220,000(0.068)

$113.33

230 113.33

$116.67

20,000 116.67

$19,883.33

2 1

1219,883.33(0.068)

$112.67

230 112.67

$117.33

19,883.33 117.33

$19,766.00

21. a. Make a table that shows the unpaid balance for each transaction date, the number of days at each unpaid balance,




September 1 $3800.00 4 $15,200.00

September 5 $3800.00 $800.00 $3000.00 4 $12,000.00

September 9 $3000.00 $40.00 $30

40.00 10 $30,400.00

September 19 $3040.00 $160.00 $3200.00 8 $25,600.00

September 27 $3200.00 $200.00 $3400.00 4 $13,600.00




$96,800.00

30$3226.67

b. Pr

($3226.67)(0.02)(1)

$64.53

I t

c. Balance due $3400.00 $64.53 $3464.53




$9736


chapter 8 consumer mathematics and financial...

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